Quantum Chromodynamics(QCD) is part of the Standard Model(SM) that describes the interaction of fundamental particles. In QCD, due to the fact that strong coupling constant is large at low energies, perturbative approaches do not work. For this reason, non-perturbative approaches have to be used for studying the properties of hadrons. Among several non-perturbative approaches, QCD sum rules is one of the reliable methods which is applied to understand the properties of hadrons and their interactions. In this thesis, the semileptonic rare decays of $B$ meson to $K_{1}(1270)$ and $K_{1} (1400)$ are analyzed in the framework of three point QCD sum rules approach. The $Brightarrow K_{1} (1270,1400) ell^+ ell^-$ decays are significant flavor changing neutral current (FCNC) decays of the $B$ meson, since FCNC processes are forbidden at tree level at SM. These decays are sensitive to the new physics beyond SM. The radiative $Brightarrow K_{1}(1270) gamma$ decay is observed experimentally. Although semileptonic $Bto K_1(1270,1400)$ decays are still not observed, they are expected to be observed at future B factories. These decays happens at the quark level with $brightarrow s ell^+ ell^- $ transition, providing new opportunities for calculating CKM matrix elements: $V_{tb}$ and $V_{ts}$. Applying three point QCD sum rules to $Brightarrow K_{1} (1270,1400) ell^+ ell^-$ decays is tricky, due to the fact that the $K_{1} (1270)$ and $K_{1} (1400)$ states are the mixtures of ideal $^{3}P_{1}(K_{1}^{A})$ and $^{1}P_{1}(K_{1}^{B})$ orbital angular momentum states. First, by taking axial vector and tensor current definitions for $K_1$ mesons, the transition form factors of $Brightarrow K_{1A} ell^+ ell^-$ and $Brightarrow K_{1B} ell^+ ell^-$ are calculated. Then using the definitions for $K_1$ mixing, the transition form factors of $Brightarrow K_{1} (1270,1400) ell^+ ell^-$ decays are obtained. The results of these form factors are used to estimate the branching ratio of $B$ meson into $K_1(1270)$ and $K_1(1400)$. The results obtained for form factors and branching fractions are also compared with the ones in the literature.

In this thesis, we investigate the masses, form factors and magnetic dipole moments of some light octet, decuplet and heavy baryons containing a single heavy quark in the framework of the light cone QCD sum rules. The magnetic dipole moments can be measured considering radiative transitions within a multiplet or between multiplets. Analyzing the transitions among the baryons and calculating the above mentioned parameters can give us insight into the structure of those baryons. In analyzing the aforementioned processes, the transition form factors play a crucial role. In this thesis, the form factors for these transitions are calculated using the light cone QCD sum rules approach. In the limit when the light quark masses are equal, mu = md = ms, QCD has an SU(3) flavour symmetry which can be used to classify the light baryons. This classification results in the light decuplet, octet and singlet baryons. The baryons containing single heavy quark, on the other hand, can be classified according to the spin of the light degrees of freedom in the heavy quark limit, mQ -&gt / infinity. QCD at low energies, when the baryons are formed, is a non-perturbative theory. Hence, for phenomenology of the baryons, the QCD sum rules as a more powerful non-perturbative approach is used. Understanding the properties of nucleons is one of the main objectives of QCD. To investigate the properties of the nucleons, the axial N-Delta(1232) transition form factors are calculated within the light cone QCD sum rules method. A comparison of our results on those form factors with the predictions of lattice QCD and quark model is presented. The nucleon electromagnetic form factors are also calculated in the same framework using the most general form of the nucleon interpolating current. Using two forms of the distribution amplitudes (DA&rsquo / s), predictions for the form factors are presented and compared with existing experimental data. It is shown that our results describe the existing experimental data remarkably well. Another important property of the baryons is their magnetic moments. The magnetic moments of the heavy Xi_Q (Q = b or c) baryons containing a single charm or bottom quark are calculated within the light cone QCD sum rules approach. A comparison of our results with the predictions of other approaches, such as relativistic and nonrelativistic quark models, hyper central model, Chiral perturbation theory, soliton and skyrmion models is presented. Moreover, inspired by the results of recent experimental discoveries for charm and bottom baryons, the masses and magnetic moments of the heavy baryons with J^2P = 3/2^+ containing a single heavy quark are studied also within the light cone QCD sum rules method. Our results on the masses of heavy baryons are in good agreement with predictions of other approaches, as well as with the existing experimental values. Our predictions on the masses of the states, which are not experimentally discovered yet, can be tested in the future experiments. A comparison of our results on the magnetic moments of these baryons and the hyper central model predictions is also presented.

Dans cette thèse, nous construisons un modèle de liaisons fortes tridimensionnel minimal pour les cuprates supraconducteurs monocouches à base de lanthane. Celui-ci prend en compte huit orbitales, dont deux d'entre elles impliquent les ions oxygène apicaux. L'optimisation des paramètres microscopiques permet de reproduire presque parfaitement la bande de conduction tridimensionnelle telle qu'elle a été obtenue à partir des calculs DFT. Nous discutons la façon dont chacun des paramètres entrant en jeu dans ce modèle multi-bandes influence la bande de conduction, et nous montrons que la forme particulière de sa dispersion contraint les valeurs des paramètres. Nous mettons alors en évidence que la détermination standard d'un modèle effectif à une bande au travers d'un traitement perturbatif converge lentement en raison de la valeur relativement faible du gap de transfert de charges. A ce stade, cela nous permet, en revanche, de lever le voile sur l'origine microscopique des amplitudes de saut des électrons au sein des plans et en-dehors des plans. Une approche alternative au calcul des paramètres microscopiques de saut du modèle effectif de liaisons fortes est présentée et mise à contribution. Il en résulte que l'accord avec la DFT est préservé à condition que les amplitudes de saut de plus longue portée soient conservées. Une comparaison avec les modèles existants est également effectuée. La surface de Fermi, mettant en exergue des domaines décalés qui alternent en taille et en forme, est comparée à l'expérience. De plus, la densité d'états du modèle est aussi calculée. Une analyse plus approfondie du modèle est réalisée au travers d'une étude en couplage faible des instabilités magnétiques. Les calculs sont effectués sur de grandes cellules et nous avons trouvé une compétition parmi plusieurs instabilités magnétiques tridimensionnelles dans la région d’intérêt du dopage en trous accessible expérimentalement. Bien qu'à notre connaissance cela ne semble pas avoir été évoqué expérimentalement, nous montrons à l'issue de notre étude, que la tendance du modèle à former des ondes de densité de spin incommensurables tridimensionnelles est la plus forte à proximité du dopage 1/8. / In this thesis, we construct a minimal three-dimensional tight-binding model for single-layer La-based cuprate superconductors. It entails eight orbitals, two of them involving apical oxygen ions. Parameter optimization allows to almost perfectly reproduce the three-dimensional conduction band as obtained from DFT. We discuss how each parameter entering this multiband model influences it, and show that the peculiar form of its dispersion severely constraints the parameter values. We then evidence that standard perturbative derivation of an effective one-band model is poorly converging because of the comparatively small value of the charge transfer gap. Yet, this allows us to unravel the microscopical origin of the in-plane and out-of-plane hopping amplitudes. An alternative approach to the computation of the tight-binding parameters of the effective model is presented and worked out. It results that the agreement with DFT is preserved provided longer-ranged hopping amplitudes are retained. A comparison with existing models is performed, too. The Fermi surface, showing staggered pieces alternating in size and shape, is compared to experiment. The density of states is calculated as well. The model is further analyzed through a weak coupling study of magnetic instabilities. It is performed on large clusters and competition between several three-dimensional magnetic instabilities in the hole-doping region of experimental interest is found. We show that the tendency to form a three-dimensional incommensurate spin density wave is strongest in the vicinity of 1/8 doping.